# PSAT Math : How to find the volume of a cylinder

## Example Questions

### Example Question #851 : Sat Mathematics

Jessica wishes to fill up a cylinder with water at a rate of  gallons per minute. The volume of the cylinder is  gallons. The hole at the bottom of the cylinder leaks out  gallons per minute. If there are  gallons in the cylinder when Jessica starts filling it, how long does it take to fill?

Explanation:

Jessica needs to fill up  gallons at the effective rate of .  divided by  is equal to . Notice how the units work out.

### Example Question #301 : Psat Mathematics

A vase needs to be filled with water.  If the vase is a cylinder that is  tall with a  radius, how much water is needed to fill the vase?

Explanation:

Cylinder

### Example Question #137 : Solid Geometry

A cylinder has a base diameter of 12 in and is 2 in tall. What is the volume?

Explanation:

The volume of a cylinder is

The diameter is given, so make sure to divide it in half.

The units are inches cubed in this example

### Example Question #11 : Cylinders

What is the volume of a cylinder with a radius of 4 and a height of 5?

Explanation:

### Example Question #11 : Cylinders

Claire's cylindrical water bottle is 9 inches tall and has a diameter of 6 inches. How many cubic inches of water will her bottle hold?

Explanation:

The volume is the area of the base times the height. The area of the base is , and the radius here is 3.

### Example Question #140 : Solid Geometry

What is the volume of a circular cylinder whose height is 8 cm and has a diameter of 4 cm?

Explanation:

The volume of a circular cylinder is given by  where  is the radius and  is the height.  The diameter is given as 4 cm, so the radius would be 2 cm as the diameter is twice the radius.

### Example Question #11 : How To Find The Volume Of A Cylinder

You have tall glass with a radius of 3 inches and height of 6 inches. You have an ice cube tray that makes perfect cubic ice cubes that have 0.5 inch sides. You put three ice cubes in your glass. How much volume do you have left for soda? The conversion factor is .

Explanation:

First we will calculate the volume of the glass. The volume of a cylinder is

Now we will calculate the volume of one ice cube:

The volume of three ice cubes is . We will then subtract the volume taken up by ice from the total volume:

Now we will use our conversion factor:

### Example Question #10 : Cylinders

A water glass has the shape of a right cylinder. The glass has an interior radius of 2 inches, and a height of 6 inches. The glass is 75% full. What is the volume of the water in the glass (in cubic inches)?

Explanation:

The volume of a right cylinder with radius  and height  is:

Since the glass is only 75% full, only 75% of the interior volume of the glass is occupied by water. Therefore the volume of the water is:

### Example Question #1 : How To Find The Volume Of A Cylinder

A circle has a circumference of  and it is used as the base of a cylinder. The cylinder has a surface area of . Find the volume of the cylinder.

Explanation:

Using the circumference, we can find the radius of the circle. The equation for the circumference is ; therefore, the radius is 2.

Now we can find the area of the circle using . The area is .

Finally, the surface area consists of the area of two circles and the area of the mid-section of the cylinder: , where  is the height of the cylinder.

Thus,  and the volume of the cylinder is .

### Example Question #11 : How To Find The Volume Of A Cylinder

A metal cylindrical brick has a height of . The area of the top is .  A circular hole with a radius of  is centered and drilled half-way down the brick. What is the volume of the resulting shape?